Name
Minnesota Comprehensive
Assessments-Series III
Mathematics Item Sampler
Grade 11
ITEM SAMPLERS ARE NOT SECURE TEST MATERIALS. THIS
ITEM SAMPLER TEST BOOK MAY BE COPIED OR DUPLICATED.
State of Minnesota
© Copyright Minnesota Department of Education
Roseville, MN 55113-4266
Grade 11 Formula Sheet
You may use the following formulas to solve problems on this
test.
2
Pythagorean Theorem
d=
Distance formula
Quadratic formula
Trigonometric Relations
–b ± b2 – 4ac
2a
opposite
hypotenuse
tan θ =
A = area
A = r 2
C = circumference
C = d
d = diameter
r = radius
SA = surface area
SA = ph + 2B
B = area of base
2
SA = r l + r
h = height
2
p = perimeter
r = radius
l = slant height
V = Bh
V = volume
V = 31 Bh
B = area of base
V = 34 r 3
h = height
r = radius
3
2
(x2 – x1)2+ (y2 – y1)2
x=
sin θ =
SA = 4r
2
a +b = c
cos θ =
opposite
adjacent
adjacent
hypotenuse
4
Mathematics Test
General Directions
• This test contains four segments.
• You may write in this test book as scratch paper. Grid paper is also provided
at the back of the test book.
• You will find a formula sheet at the beginning of this test book. You may tear
it out of your test book to use while taking the test.
• For each question, choose the answer you think is best.
• Look at the sample questions that show how the different types of questions
should be answered.
Multiple-choice Question Answered in Test Book:
20 − 8 =
•
A.
8
B.
10
C.
12
D.
16
Answer each fill in the blank question by writing your answer in the space
below the question. You may only use the digits 0–9 and the symbols for
fraction (/), decimal (.), and a negative sign (–). Do not include a label on
your answer. If your answer is a mixed number you must change it to an
improper fraction or a decimal.
Fill in the Blank Question Answered in Test Book:
1
4
11
4
• You may use a calculator for all segments.
• When you finish a segment of the test, stop and check your answers. Then use
the sticker given to you to seal it. Once you seal a segment, you cannot go back
to it. Each segment must be sealed before you move on to the next segment.
The General Direction page is the same as it appears in the test. The item
sampler will only have 2 segments.
5
On this test, do your own best work to show what you know and can do.
•
Do not accept help finding answers to test questions.
•
Do not give answers to other students.
•
Do not tell others what is on the test.
•
There may be consequences if you do not follow directions or if you
behave dishonestly.
6
Put sticker here
Segment 1
You will be told when to begin this
segment.
You MAY use a calculator for this
segment.
7
Mathematics Test — Segment 1
1
1. The population of a type of bacteria doubles every 3.5 hours. Which expression
is a reasonable approximation of how many bacteria there will be in 20 hours for
an initial population, P, of bacteria?
A.
B.
C.
D.
P
2P
50P
64P
966
2. The graph of y=f(x) is shown.
y
4
3
2
1
-2 -1 0
-1
1 2 3 4 5
x
What is a value of x for which f(x)=4?
A.
B.
C.
D.
1
1.5
4
5
967
ITEM SAMPLER.
MAY BE DUPLICATED.
8
Go on to the next page.
3. How many solutions does
A.
B.
C.
D.
have?
1
0
1
2
4
969
4. For which equation is y a function of x?
A.
B.
2
C. y =x–2
2
2
D. y =4–x
970
ITEM SAMPLER.
MAY BE DUPLICATED.
9
Go on to the next page.
1
5. What is the domain of f(x)=
?
A.
B.
C.
D.
971
6. The graph of a function is shown.
y
4
3
2
1
-4 -3 -2 -1 0
-1
-2
-3
-4
1 2 3 4
x
Which statement is true about the rate of change for this function when
–3 < x < 0?
A.
B.
C.
D.
The
The
The
The
rate
rate
rate
rate
of
of
of
of
change
change
change
change
is
is
is
is
constant.
decreasing.
increasing.
negative.
972
ITEM SAMPLER.
MAY BE DUPLICATED.
10
Go on to the next page.
7. Emma takes a job with a starting salary of $42,000. Her salary increases
by 4% at the beginning of each year. What will be Emma’s salary, to the
nearest thousand dollars, at the beginning of year 10?
A.
B.
C.
D.
$57,000
$59,000
$60,000
$62,000
974
8. Divide.
3
2
(2x +9x –11x–24)÷(x–2)
What is the remainder?
A.
B.
C.
D.
0
2
6
18
976
ITEM SAMPLER.
MAY BE DUPLICATED.
11
Go on to the next page.
1
1
9. A root of function f(x) is –1–2i. Which could be an equation for this function?
A.
B.
C.
D.
f(x)=x2 –2x–3
2
f(x)=x –2x+5
f(x)=x2 +2x–3
2
f(x)=x +2x+5
977
Please write your answer in the space below the question. You may use the
digits: 0-9 and the symbols: slash for a fraction bar (/), a decimal (.), and a
negative sign (-). If your answer is a mixed number you must change it to
an improper fraction or a decimal.
10. Tuan wants to make the rectangular frame shown.
10 cm
13 cm
Opening
x cm
x cm
978
It will be 10 centimeters wide and 13 centimeters long. He wants his frame to
have a uniform width, x, and a rectangular opening. For what value of x is the
2
area of the opening inside the frame 70 cm ?
ITEM SAMPLER.
MAY BE DUPLICATED.
12
Go on to the next page.
11. A scientist begins an experiment with 800 bacteria cells. After each 10-hour
period, only
the bacteria cells remain. Let t be the number of hours since the
beginning of the experiment. Which equation could be used to represent the
situation when only 200 bacteria cells remain?
A.
B.
C.
D.
979
12. Which number is an extraneous solution of the equation
A.
B.
C.
D.
?
–6
–2
0
3
981
ITEM SAMPLER.
MAY BE DUPLICATED.
13
Go on to the next page.
1
Put sticker here
This is the end of Segment 1.
Check your work. Then seal this
segment.
14
You will be told when to begin this
segment.
You MAY use a calculator for this
segment.
15
Put sticker here
Segment 2
Mathematics Test — Segment 2
2
13. The surface area of a baseball is 177 cm . What is the diameter of the baseball?
(Use 3.14 for .)
A.
B.
C.
D.
3.75 cm
7 cm
7.5 cm
14.1 cm
982
2
14. Triangle RST is shown.
S
4x
x+2
R
How many units long is
A.
B.
C.
D.
3x + 4
T
?
2
3
4
12
984
ITEM SAMPLER.
MAY BE DUPLICATED.
16
Go on to the next page.
15. Line m is parallel to line n.
m
n
Y
42°
X
144° Z
Not drawn to scale
2
What is the measure of
A.
B.
C.
D.
XYZ?
36°
42°
78°
102°
985
Please write your answer in the space below the question. You may use the
digits: 0-9 and the symbols: slash for a fraction bar (/), a decimal (.), and a
negative sign (-). If your answer is a mixed number you must change it to
an improper fraction or a decimal.
16. Roads connecting the towns of Oceanside, River City, and Lake View form a
triangle. The distance from Oceanside to River City is 38 kilometers. The
distance from River City to Lake View is 26 kilometers. What is the smallest
possible whole number of kilometers between Lake View and Oceanside?
986
ITEM SAMPLER.
MAY BE DUPLICATED.
17
Go on to the next page.
17. In figure RSTU,
and
intersect at point M, so that
and
is
parallel to
. Which additional information is needed to prove that figure RSTU
is a rectangle?
A.
B.
C.
D.
987
2
Please write your answer in the space below the question. You may use the
digits: 0-9 and the symbols: slash for a fraction bar (/), a decimal (.), and a
negative sign (-). If your answer is a mixed number you must change it to
an improper fraction or a decimal.
18. Maggie and Wei are measuring the distance across a circular fountain indirectly
as shown in the diagram.
S
T
R
F
They find that the length of
is 15 meters and the length of
is 9 meters.
is tangent to circle F and point T is on
. To the nearest meter, what is the
diameter of the fountain?
88
9ITEM SAMPLER.
MAY BE DUPLICATED.
18
Go on to the next page.
19. Twelve students are lined up to have their class picture taken.
26 ft.
52°
2
The photographer’s camera has a picture angle of 52°. The picture angle limits the
width of the photo that can be taken. The line of students is approximately 26 feet
long. About how far must the photographer be from the line of students in order
to center all 12 students in the picture?
A.
B.
C.
D.
15
27
30
53
feet
feet
feet
feet
989
ITEM SAMPLER.
MAY BE DUPLICATED.
19
Go on to the next page.
20. An archaeologist used string to make a grid over an area where she was
digging. She discovered a bowl buried at (1, 4) and a tool at (3, 10) on her grid.
She suspected that an item was buried at the midpoint of the segment
connecting the bowl and the tool. At which position on her grid should the
archaeologist dig to look for the buried item?
A. (1, 3)
B. (2, 7)
C.
D. (4, 14)
2
991
Please write your answer in the space below the question. You may use the
digits: 0-9 and the symbols: slash for a fraction bar (/), a decimal (.), and a
negative sign (-). If your answer is a mixed number you must change it to
an improper fraction or a decimal.
21. A group of health care providers consists of 4 doctors, 3 dentists, and 5 nurses.
How many combinations of 2 health care providers of different types are possible?
992
22. Isabella flipped a fair coin 100 times. Which statement about Isabella’s
outcomes is most likely true?
A. The coin landed heads up 50 times and tails up 50 times.
B. The number of times the coin landed heads up was less than 50.
C. If Isabella continues to flip the coin, the experimental probability of the
coin landing heads up will increase.
D. If Isabella continues to flip the coin, the experimental probability of the
coin landing heads up will approach .
993
ITEM SAMPLER.
MAY BE DUPLICATED.
20
Go on to the next page.
Please write your answer in the space below the question. You may use
the digits: 0-9 and the symbols: slash for a fraction bar (/), a decimal (.),
and a negative sign (-). If your answer is a mixed number you must change
it to an improper fraction or a decimal.
23. Eli receives a shipment of 40 new books for his bookstore: 5 biographies,
12 mysteries, 10 romances, 11 technical books, and 2 cookbooks. Eli randomly
picks 2 books from the shipment. What is the probability that he picks a
biography first and then picks a technical book?
994
2
24. Reginald is designing an outdoor art exhibit. He needs a metal equilateral
triangle that measures 40 inches on each side. He wants to cut the triangle from
a rectangular piece of metal that is 40 inches long. What is the minimum width
of the rectangle Reginald needs to be able to cut out the triangle?
A.
inches
B.
inches
C.
inches
D. 40 inches
995
ITEM SAMPLER.
MAY BE DUPLICATED.
21
Go on to the next page.
Put sticker here
This is the end of Segment 2.
Check your work. Then seal this
segment.
22
ITEM SAMPLERS ARE NOT SECURE TEST MATERIALS. THIS
ITEM SAMPLER TEST BOOK MAY BE COPIED OR DUPLICATED.
Grade 11 Teacher’s Guide
MCA Item Sampler
Teacher’s Guide
[email protected]
An Introduction to the MCA
The Minnesota Comprehensive Assessments are reading, mathematics and
science tests that help schools and districts measure student progress toward
the state’s academic standards. The grades 3–8 mathematics assessments
became operational in 2011 as the Minnesota Comprehensive AssessmentsSeries III (MCA-III) and are aligned to the 2007 Minnesota Academic
Standards. In 2012, the science assessments became operational as the
Minnesota Comprehensive Assessments-Series III (MCA-III) and are aligned
to the 2009 Minnesota Academic Standards. In 2013, the grades 3-8 and 10
reading assessments are aligned to the 2010 Minnesota Academic Standards
as the Minnesota Comprehensive Assessments-Series III (MCA-III). In 2014,
the grade 11 mathematics assessment is aligned to the 2007 Minnesota
Academic Standards as the Minnesota Comprehensive Assessments-Series III
(MCA-III).
The Purpose of the MCA Item Samplers
An item sampler is not a complete test. It contains a smaller number of the
items that students will see on a full-length test in the spring. The MCA Item
Samplers were developed to familiarize students and teachers with the format
of the MCA and the kinds of items that will appear on them.
This MCA Item Sampler is not a real test. It should not be used to predict
how well students will do on the tests. However, students may feel more
comfortable with the tests if they have reviewed the Item Samplers prior to
the test.
How the MCA Item Samplers Were Created
The Item Samplers mirror the format of the MCA. The
student directions, segment layouts, and answer sheet each
reflect the way the test will look in the spring, except that the
Item Sampler is shorter than the actual test. As with all MCAs,
the reading passages and the math and reading questions
have been thoroughly reviewed by Minnesota teachers prior to
testing. Minnesota students have answered these questions
Go on toonthe
previous tests.
25
next page.
Grade 11 Teacher’s Guide
The distribution of question types and their aligned content selected for the Item
Sampler generally reflects a range of items from each strand in the Minnesota
Academic Standards. Whenever possible, the Item Samplers have the following
designs:
Math:
•
•
•
•
Two segments
o All Grade 11 segments allow for the use of a calculator.
o The actual MCA has four segments.
Approximately nineteen multiple-choice items
Five gridded-response items
Formula sheet
The Contents of This Teacher’s Guide
The Answer Key identifies the answers and solutions to the questions. It
also identifies the strand/sub-strand/benchmark from the Minnesota
Academic Standards for the question.
State Standards & Test Specifications
The Item Samplers are primarily intended to familiarize teachers and students
with the format of the MCA. The best preparation for the content of the MCA
is done as a part of your curriculum planning. When doing that, reference the
Minnesota Academic Standards and the test specifications for the MCA. For further
questions about the MCAs, email us at [email protected].
26
Grade 11 Teacher’s Guide
Mathematics MCA Item Sampler Answer Key
Grade 11 Math
Item #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Correct Answer
C
D
B
A
C
B
C
C
D
Grid
B
B
C
D
C
Grid
C
Grid
B
B
Grid
D
Grid
C
Item
Type
MC
MC
MC
MC
MC
MC
MC
MC
MC
GR
MC
MC
MC
MC
MC
GR
MC
GR
MC
MC
GR
MC
GR
MC
27
Strand Standard Benchmark
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
4
4
4
3
4
1
3
1
1
1
2
3
3
4
4
4
1
4
3
3
3
3
4
4
3
3
3
3
08
01
07
02
03
08
05
02
05
01
02
07
01
07
01
03
07
08
02
04
01
03
05
05
Grade 11 Teacher’s Guide
Grade 3 Teacher’s Guide
Item # — The number of the question in the Item Sampler.
Correct Answer — Answers to multiple-choice questions are listed.
Item Type — Multiple Choice (MC) and Gridded Response (GR)
Strand — In mathematics, the MCA-III measures four strands:
1.
2.
3.
4.
Number and Operation
Algebra
Geometry and Measurement
Data Analysis and Probability
Standard — Each strand has one or more standards
Benchmark — Each standard has one or more benchmarks. See the
cation for further explanation of
Academic Standards or test sp
each benchmark.
28
1106180
ISD15553